code: def test_ddm_ilu():
      A = []
      Alu = []
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == []
  
      A = [[]]
      Alu = [[]]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == []
  
      A = [[QQ(1), QQ(2)], [QQ(3), QQ(4)]]
      Alu = [[QQ(1), QQ(2)], [QQ(3), QQ(-2)]]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == []
  
      A = [[QQ(0), QQ(2)], [QQ(3), QQ(4)]]
      Alu = [[QQ(3), QQ(4)], [QQ(0), QQ(2)]]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == [(0, 1)]
  
      A = [
          [QQ(1), QQ(2), QQ(3)],
          [QQ(4), QQ(5), QQ(6)],
          [QQ(7), QQ(8), QQ(9)],
      ]
      Alu = [
          [QQ(1), QQ(2), QQ(3)],
          [QQ(4), QQ(-3), QQ(-6)],
          [QQ(7), QQ(2), QQ(0)],
      ]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == []
  
      A = [
          [QQ(0), QQ(1), QQ(2)],
          [QQ(0), QQ(1), QQ(3)],
          [QQ(1), QQ(1), QQ(2)],
      ]
      Alu = [
          [QQ(1), QQ(1), QQ(2)],
          [QQ(0), QQ(1), QQ(3)],
          [QQ(0), QQ(1), QQ(-1)],
      ]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == [(0, 2)]
  
      A = [[QQ(1), QQ(2), QQ(3)], [QQ(4), QQ(5), QQ(6)]]
      Alu = [[QQ(1), QQ(2), QQ(3)], [QQ(4), QQ(-3), QQ(-6)]]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == []
  
      A = [[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]]
      Alu = [[QQ(1), QQ(2)], [QQ(3), QQ(-2)], [QQ(5), QQ(2)]]
      swaps = ddm_ilu(A)
      assert A == Alu
      assert swaps == []
  
file_path: sympy/sympy/polys/matrices/tests/test_dense.py
imports: from sympy.testing.pytest import raises
  from sympy.polys import ZZ, QQ
  from sympy.polys.matrices.ddm import DDM
  from sympy.polys.matrices.dense import ddm_transpose, ddm_iadd, ddm_isub, ddm_ineg, ddm_imatmul, ddm_imul, ddm_irref, ddm_idet, ddm_iinv, ddm_ilu, ddm_ilu_split, ddm_ilu_solve, ddm_berk
  from sympy.polys.matrices.exceptions import DMDomainError, DMNonInvertibleMatrixError, DMNonSquareMatrixError, DMShapeError
label_desc: Use image node_id 10 for calling a global function with example usage: test_ddm_ilu() without return types